I did it, I went to the city and tried three different free wifi networks in shoping centres, but it was the same. I think that problem will not be in my home network.

Darn, I was hoping it would end up being something simple, but at least now Amazon has to deal with it because it's definitely a Kindle problem. I'm pretty sure at this point they will have no choice but to replace it, unless they can figure out why their server seems to be refusing to authenticate your Kindle's communication. They're usually really good about returns, but the time and process involved depends on where you are.